Estimates of Sin at our sites from the clear sky and cloudy sky model simulations
bracket our tower observations (fig. S5). We then solved for the clear sky and cloudy sky
fractions each month that matched our monthly observations of Sin. These fractions were
then used to combine the clear sky and cloudy sky model estimates of tropopause net
radiation from the control and burn albedo simulations. Finally, we took the difference
between tropopause net radiation between the control and burn albedo simulations
(weighted by the appropriate clear sky and cloudy sky fractions) as our estimate of
instantaneous radiative forcing at the tropopause (fig. S8). Based on a series of published
climate simulations (2, 3) we assumed that stratospheric adjustment to changes in surface
albedo was negligible and so the instantaneous forcing at the tropopause was equal to the
IPCC definition of adjusted radiative forcing. In this analysis, we found that the
difference in annual outgoing shortwave radiation at the tropopause was 60% of the
difference in outgoing shortwave radiation at the surface.